Problem: Solve for $x$ and $y$ using elimination. ${-2x+3y = -8}$ ${3x+y = 34}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-3$ ${-2x+3y = -8}$ $-9x-3y = -102$ Add the top and bottom equations together. $-11x = -110$ $\dfrac{-11x}{{-11}} = \dfrac{-110}{{-11}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {-2x+3y = -8}\thinspace$ to find $y$ ${-2}{(10)}{ + 3y = -8}$ $-20+3y = -8$ $-20{+20} + 3y = -8{+20}$ $3y = 12$ $\dfrac{3y}{{3}} = \dfrac{12}{{3}}$ ${y = 4}$ You can also plug ${x = 10}$ into $\thinspace {3x+y = 34}\thinspace$ and get the same answer for $y$ : ${3}{(10)}{ + y = 34}$ ${y = 4}$